Characterization and Detection of Loops in n-Dimensional Discrete Toric Spaces
نویسندگان
چکیده
Toric spaces being non-simply connected, it is possible to find in such spaces some loops which are not homotopic to a point: we call them toric loops. Some applications, such as the study of the relationship between the geometrical characteristics of a material and its physical properties, rely on three dimensional discrete toric spaces and require detecting objects having a toric loop. In this work, we study objects embedded in discrete toric spaces, and propose a new definition of loops and equivalence of loops. Moreover, we introduce a characteristic of loops that we call wrapping vector : relying on this notion, we propose a linear time algorithm which detects whether an object has a toric loop or not.
منابع مشابه
Characterizing and Detecting Toric Loops in n-Dimensional Discrete Toric Spaces
Toric spaces being non-simply connected, it is possible to find in such spaces some loops which are not homotopic to a point: we call them toric loops. Some applications, such as the study of the relationship between the geometrical characteristics of a material and its physical properties, rely on three-dimensional discrete toric spaces and require detecting objects having a toric loop. In thi...
متن کاملDouble-null operators and the investigation of Birkhoff's theorem on discrete lp spaces
Doubly stochastic matrices play a fundamental role in the theory of majorization. Birkhoff's theorem explains the relation between $ntimes n$ doubly stochastic matrices and permutations. In this paper, we first introduce double-null operators and we will find some important properties of them. Then with the help of double-null operators, we investigate Birkhoff's theorem for descreate $l^p$ sp...
متن کاملFault Strike Detection Using Satellite Gravity Data Decomposition by Discrete Wavelets: A Case Study from Iran
Estimating the gravity anomaly causative bodies boundary can facilitate the gravity field interpretation. In this paper, 2D discrete wavelet transform (DWT) is employed as a method to delineate the boundary of the gravity anomaly sources. Hence, the GRACE’ satellite gravity data is decomposed using DWT. DWT decomposites a single approximation coefficients into four distinct components: the appr...
متن کاملDiscrete Time Control Method for SVM Direct Active Power and Stator Flux Control of PMSG-Based Wind Turbine
This paper proposes a new method for direct control of active power and stator flux of permanent magnet synchronous generator (PMSG) used in the wind power generation system. Active power and stator flux are controlled by the proposed discrete time algorithm. Despite the commonly used vector control methods, there is no need for inner current control loops. To decrease the errors between refere...
متن کاملManifolds of G 2 Holonomy from N = 4 Sigma Model
Using two dimensional (2D) N = 4 sigma model, with U(1) gauge symmetry, and introducing the ADE Cartan matrices as gauge matrix charges, we build ” toric” hyperKahler eight real dimensional manifolds X8. Dividing by one toric geometry circle action of X8 manifolds, we present examples describing quotients X7 = X8 U(1) of G2 holonomy. In particular, for the Ar Cartan matrix, the quotient space i...
متن کامل